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\title{Master of Science in Applied Mathematical Analysis and Bachelor in Computer Science seeks PhD position. }
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My name is Mathias Andersen, I am 28 years old, live in Aalborg and is currently studying computer science at Aalborg university. It is my hope that you will consider me for one of the vacant PhD positions. 
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In 2008 i graduated from Aalborg University and received my masters degree in mathematical analysis. My master thesis is titled "Regularity of Solutions to Schr\"{o}dingers Equation with the Coulomb Potential". The most important result in the thesis is that a solution to the Schr\"{o}dinger equation is actually continuous. The thesis is an expanded version of another article by Thomas Østergaard Sørensen. 

After graduating I worked as a math teacher in Randers Statsskole Gymnasium, and later worked as a web developer in the Nørresundby based company UVdata. Then in 2010 I started studying computer science at Aalborg University and will become a bachelor in computer science this summer.
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I am currently working on an interesting project in the domain of formal verification. The reader might be familiar with the tool TAPAAL; it is a modelling, simulation and verification tool for timed-arc Petri nets, developed at Aalborg University. When we perform formal verification on the subset of timed-arc Petri nets that has only non-strict age guards we only have to consider integer delays. The goal of the project is to develop a formal discrete semantics for timed-arc Petri nets and to design an efficient algorithm for verification. This algorithm will be implemented in c++, and it is our goal that it will be able to perform verification faster than the original algorithm.
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I would like to do research in the field of formal verification of hybrid systems. This is a very active research area and the theory relies on mathematical analysis, in particular the study of differential equations. A large portion of my studies at the institute of mathematics at Aalborg university was devoted to differential equations, function spaces, operators etc., and thus it is a field in which I am particularly skilled. 

I have good programming skills. During the DAT2 semester my project group implemented an interpreter for a mathematical programming language that we had designed ourselves. The interpreter is implemented in Java and the language is a mix of Matlab, bc and Maple where the focus is on conveniently performing matrix manipulations. The programming language is not as sophisticated as neither Matlab or Maple, but it is quite convenient to use for small tasks involving matrix operations. I like to construct tools that can be put to practical use. As mentioned above I am currently coding in c++.
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My motivation for seeking a PhD position is that I enjoy working on open and challenging problems and my favourite thing about scientific research is that we move around in uncharted territory and make up the rules as we go along. I am also fond of having a mix of programming tasks and theoretical work. 

I am quite open about what kind of projects to work on in connection with a PhD study. My main priority is to be involved in serious research and it would be nice if I could put my experience in the field of mathematical analysis to good use. 
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Mathias Andersen


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